梯度微粒群优化算法及其收敛性分析

针对标准微粒群优化算法微粒运动轨迹的收敛性进行了分析.给出并证明了微粒运动轨迹收敛的充分条件.提出一种简便的等高线图判别法,该方法能够通过参数的位置判断微粒轨迹是否收敛并衡量收敛速度.为提高算法的收敛速度.构造出一种梯度微粒群优化算法,给出并证明了该方法收敛的充分条件.仿真结果表明,梯度微粒群优化算法具有优良的搜索性能.     

Cellular particle swarm optimization

This paper proposes a cellular particle swarm optimization (CPSO), hybridizing cellular automata (CA) and particle swarm optimization (PSO) for function optimization. In the proposed CPSO, a mechanism of CA is integrated in the velocity update to modify the trajectories of particles to avoid being trapped in the local optimum. With two different ways of integration of CA and PSO, two versions of CPSO, i.e. CPSO-inner and CPSO-outer, have been discussed. For the former, we devised three typical lattice structures of CA used as neighborhood, enabling particles to interact inside the swarm; and for the latter, a novel CA strategy based on “smart-cell” is designed, and particles employ the information from outside the swarm. Theoretical studies are made to analyze the convergence of CPSO, and numerical experiments are conducted to compare the proposed algorithm with different variants of PSO. According to the experimental results, the proposed method performs better than other variants of PSO on benchmark test functions.     

Improved global-best-guided particle swarm optimization with learning operation for global optimization problems

In this paper, an improved global-best-guided particle swarm optimization with learning operation (IGPSO) is proposed for solving global optimization problems. The particle population is divided into current population, historical best population and global best population, and each population is assigned a corresponding searching strategy. For the current population, the global neighborhood exploration strategy is employed to enhance the global exploration capability. A local learning mechanism is used to improve local exploitation ability in the historical best population. Furthermore, stochastic learning and opposition based learning operations are employed to the global best population for accelerating convergence speed and improving optimization accuracy. The effects of the relevant parameters on the performance of IGPSO are assessed. Numerical experiments on some well-known benchmark test functions reveal that IGPSO algorithm outperforms other state-of-the-art intelligent algorithms in terms of accuracy, convergence speed, and nonparametric statistical significance. Moreover, IGPSO performs better for engineering design optimization problems.     

Unified particle swarm delivers high efficiency to particle swarm optimization

This paper suggests integrating a unification factor into particle swarm optimization (PSO) to balance the effects of cognitive and social terms. The resultant unified particle swarm (UPS) moves particles toward the center of its personal best and the global best. This improves on PSO, which moves particles far beyond the center. Widely used benchmark functions and four types of experiments demonstrate that the proposed UPS uses slightly more computational time than PSO to attain significantly higher efficiency and, usually, better solution effectiveness and consistency than PSO. Robust performance was further demonstrated by the significantly higher efficiency and better solution effectiveness and stability achieved by the UPS, as compared to the PSO and its variants. Outstandingly, convergence speeds for the proposed UPS were very good on the 13 benchmark functions examined in experiment 1, demonstrating the correct movement of UPS particles toward convergence.     

Analysis of particle interaction in particle swarm optimization

In this paper, we analyze the behavior of particle swarm optimization (PSO) on the facet of particle interaction. We firstly propose a statistical interpretation of particle swarm optimization in order to capture the stochastic behavior of the entire swarm. Based on the statistical interpretation, we investigate the effect of particle interaction by focusing on the social-only model and derive the upper and lower bounds of the expected particle norm. Accordingly, the lower and upper bounds of the expected progress rate on the sphere function are also obtained. Furthermore, the sufficient and necessary condition for the swarm to converge is derived to demonstrate the PSO convergence caused by the effect of particle interaction.     

一种基于种群速度的自适应粒子群算法

分析了粒子群算法的收敛性,指出早熟是由于粒子速度降低而失去继续搜索可行解的能力.进而提出一种基于种群速度动态改变惯性权重的粒子群算法,该算法以种群粒子平均速度为信息动态改变惯性权重,避免了粒子速度过早接近0.通过5个标准测试函数的仿真实验并与其他算法相比,结果表明该算法在进化中期能很好地保持种群多样性,有效地改善算法的平均最优值和成功率.     

A perturbed particle swarm algorithm for numerical optimization

The canonical particle swarm optimization (PSO) has its own disadvantages, such as the high speed of convergence which often implies a rapid loss of diversity during the optimization process, which inevitably leads to undesirable premature convergence. In order to overcome the disadvantage of PSO, a perturbed particle swarm algorithm (pPSA) is presented based on the new particle updating strategy which is based upon the concept of perturbed global best to deal with the problem of premature convergence and diversity maintenance within the swarm. A linear model and a random model together with the initial max–min model are provided to understand and analyze the uncertainty of perturbed particle updating strategy. pPSA is validated using 12 standard test functions. The preliminary results indicate that pPSO performs much better than PSO both in quality of solutions and robustness and comparable with GCPSO. The experiments confirm us that the perturbed particle updating strategy is an encouraging strategy for stochastic heuristic algorithms and the max–min model is a promising model on the concept of possibility measure.     

A hybrid algorithm based on particle swarm and chemical reaction optimization

In this paper, a hybrid method for optimization is proposed, which combines the two local search operators in chemical reaction optimization with global search ability of for global optimum. This hybrid technique incorporates concepts from chemical reaction optimization and particle swarm optimization, it creates new molecules (particles) either operations as found in chemical reaction optimization or mechanisms of particle swarm optimization. Moreover, some technical bound constraint handling has combined when the particle update in particle swarm optimization. The effects of model parameters like InterRate, γ, Inertia weight and others parameters on performance are investigated in this paper. The experimental results tested on a set of twenty-three benchmark functions show that a hybrid algorithm based on particle swarm and chemical reaction optimization can outperform chemical reaction optimization algorithm in most of the experiments. Experimental results also indicate average improvement and deviate over chemical reaction optimization in the most of experiments.     

A discrete version of particle swarm optimization for flowshop scheduling problems

Particle swarm optimization (PSO) is a novel metaheuristic inspired by the flocking behavior of birds. The applications of PSO to scheduling problems are extremely few. In this paper, we present a PSO algorithm, extended from discrete PSO, for flowshop scheduling. In the proposed algorithm, the particle and the velocity are redefined, and an efficient approach is developed to move a particle to the new sequence. To verify the proposed PSO algorithm, comparisons with a continuous PSO algorithm and two genetic algorithms are made. Computational results show that the proposed PSO algorithm is very competitive. Furthermore, we incorporate a local search scheme into the proposed algorithm, called PSO-LS. Computational results show that the local search can be really guided by PSO in our approach. Also, PSO-LS performs well in flowshop scheduling with total flow time criterion, but it requires more computation times.     

一种基于栅格的动态粒子数微粒群算法

微粒群算法的全局搜索性能容易受到局部极值点的影响,对此,提出一种基于栅格的动态粒子数微粒群算法(GB-DPPPSO).通过设计栅格信息更新策略、粒子产生策略和粒子消灭策略,可以根据种群搜索情况动态控制粒子数变化,以保持种群多样性,提高全局搜索性能,通过对4个典型数学验证函数的仿真实验,表明了该算法相对于DPPPSO)在全局搜索成功率和搜索效率两方面均有明显改进.     

A new particle swarm optimization for the open shop scheduling problem

This paper presents a new particle swarm optimization (PSO) for the open shop scheduling problem. Compared with the original PSO, we modified the particle position representation using priorities, and the particle movement using an insert operator. We also implemented a modified parameterized active schedule generation algorithm (mP-ASG) to decode a particle position into a schedule. In mP-ASG, we can reduce or increase the search area between non-delay schedules and active schedules by controlling the maximum delay time allowed. Furthermore, we hybridized our PSO with beam search. The computational results show that our PSO found many new best solutions of the unsolved problems.     

一种多样性控制的粒子群优化算法

针对粒子群优化(PSO)算法的早熟收敛问题,提出一种新的基于群体多样性控制的PSO算法(DCPSO).该方法使得粒子在收缩状态下充分搜索,在发散状态下能够飞离群体的聚集位置,不断的收缩-发散过程保证了群体能在较大的空间进行搜索,减少了粒子群算法的早熟收敛现象.通过对多个标准测试函数的实验结果表明,DCPSO算法在复杂优化问题中具有较强的全局搜索能力,而且比现有的多样性指导的PSO算法(ARPSO)具有更好的性能.     

一种精英退火微粒群算法

提出一种针对部分较优微粒进行退火操作的精英退火微粒群算法.在退火操作中,结合Logistic方程的特点设计了一种新的错位调整方式,对当前已知最优区域重点搜索.该算法能增强算法的探索和开发能力,避免计算量过度增加.典型测试函数结果显示,该方法可同时提高算法的搜索速度和搜索精度.将基于该方法的PID控制器应用于发电机电压调节系统(AVR),计算结果表明,该PID控制器可以获得更为满意的控制性能指标.     

A modified particle swarm optimization via particle visual modeling analysis

A particle is treated as a whole individual in all researches on particle swarm optimization (PSO) currently, these are not concerned with the information of every particle’s dimensional vector. A visual modeling method describing particle’s dimensional vector behavior is presented in this paper. Based on the analysis of visual modeling, the reason for premature convergence and diversity loss in PSO is explained, and a new modified algorithm is proposed to ensure the rational flight of every particle’s dimensional component. Meanwhile, two parameters of particle-distribution-degree and particle-dimension-distance are introduced into the proposed algorithm in order to avoid premature convergence. Simulation results of the new PSO algorithm show that it has a better ability of finding the global optimum, and still keeps a rapid convergence as with the standard PSO.     

A review of particle swarm optimization. Part I: background and development

Particle Swarm Optimization (PSO), in its present form, has been in existence for roughly a decade, with formative research in related domains (such as social modelling, computer graphics, simulation and animation of natural swarms or flocks) for some years before that; a relatively short time compared with some of the other natural computing paradigms such as artificial neural networks and evolutionary computation. However, in that short period, PSO has gained widespread appeal amongst researchers and has been shown to offer good performance in a variety of application domains, with potential for hybridisation and specialisation, and demonstration of some interesting emergent behaviour. This paper aims to offer a compendious and timely review of the field and the challenges and opportunities offered by this welcome addition to the optimization toolbox. Part I discusses the location of PSO within the broader domain of natural computing, considers the development of the algorithm, and refinements introduced to prevent swarm stagnation and tackle dynamic environments. Part II considers current research in hybridisation, combinatorial problems, multicriteria and constrained optimization, and a range of indicative application areas.     

A hybrid particle swarm optimization for job shop scheduling problem

A hybrid particle swarm optimization (PSO) for the job shop problem (JSP) is proposed in this paper. In previous research, PSO particles search solutions in a continuous solution space. Since the solution space of the JSP is discrete, we modified the particle position representation, particle movement, and particle velocity to better suit PSO for the JSP. We modified the particle position based on preference list-based representation, particle movement based on swap operator, and particle velocity based on the tabu list concept in our algorithm. Giffler and Thompson’s heuristic is used to decode a particle position into a schedule. Furthermore, we applied tabu search to improve the solution quality. The computational results show that the modified PSO performs better than the original design, and that the hybrid PSO is better than other traditional metaheuristics.     

Dispersed particle swarm optimization

In particle swarm optimization (PSO) literatures, the published social coefficient settings are all centralized control manner aiming to increase the search density around the swarm memory. However, few concerns the useful information inside the particles' memories. Thus, to improve the convergence speed, we propose a new setting about social coefficient by introducing an explicit selection pressure, in which each particle decides its search direction toward the personal memory or swarm memory. Due to different adaptation, this setting adopts a dispersed manner associated with its adaptive ability. Furthermore, a mutation strategy is designed to avoid premature convergence. Simulation results show the proposed strategy is effective and efficient.     

An improved vector particle swarm optimization for constrained optimization problems

Increasing attention is being paid to solve constrained optimization problems (COP) frequently encountered in real-world applications. In this paper, an improved vector particle swarm optimization (IVPSO) algorithm is proposed to solve COPs. The constraint-handling technique is based on the simple constraint-preserving method. Velocity and position of each particle, as well as the corresponding changes, are all expressed as vectors in order to present the optimization procedure in a more intuitively comprehensible manner. The NVPSO algorithm [30], which uses one-dimensional search approaches to find a new feasible position on the flying trajectory of the particle when it escapes from the feasible region, has been proposed to solve COP. Experimental results showed that searching only on the flying trajectory for a feasible position influenced the diversity of the swarm and thus reduced the global search capability of the NVPSO algorithm. In order to avoid neglecting any worthy position in the feasible region and improve the optimization efficiency, a multi-dimensional search algorithm is proposed to search within a local region for a new feasible position. The local region is composed of all dimensions of the escaped particle’s parent and the current positions. Obviously, the flying trajectory of the particle is also included in this local region. The new position is not only present in the feasible region but also has a better fitness value in this local region. The performance of IVPSO is tested on 13 well-known benchmark functions. Experimental results prove that the proposed IVPSO algorithm is simple, competitive and stable.     

A novel particle swarm optimization algorithm with Levy flight

Particle swarm optimization (PSO) is one of the well-known population-based techniques used in global optimization and many engineering problems. Despite its simplicity and efficiency, the PSO has problems as being trapped in local minima due to premature convergence and weakness of global search capability. To overcome these disadvantages, the PSO is combined with Levy flight in this study. Levy flight is a random walk determining stepsize using Levy distribution. Being used Levy flight, a more efficient search takes place in the search space thanks to the long jumps to be made by the particles. In the proposed method, a limit value is defined for each particle, and if the particles could not improve self-solutions at the end of current iteration, this limit is increased. If the limit value determined is exceeded by a particle, the particle is redistributed in the search space with Levy flight method. To get rid of local minima and improve global search capability are ensured via this distribution in the basic PSO. The performance and accuracy of the proposed method called as Levy flight particle swarm optimization (LFPSO) are examined on well-known unimodal and multimodal benchmark functions. Experimental results show that the LFPSO is clearly seen to be more successful than one of the state-of-the-art PSO (SPSO) and the other PSO variants in terms of solution quality and robustness. The results are also statistically compared, and a significant difference is observed between the SPSO and the LFPSO methods. Furthermore, the results of proposed method are also compared with the results of well-known and recent population-based optimization methods.     

A parameter selection strategy for particle swarm optimization based on particle positions

In this study, we found that engineering experience can be used to determine the parameters of an optimization algorithm. We came to this conclusion by analyzing the dynamic characteristics of PSO through a large number of experiments. We constructed a relationship between the dynamic process of particle swarm optimization and the transition process of a control system. A novel parameter strategy for PSO was proven in this paper using the overshoot and the peak time of a transition process. This strategy not only provides a series of flexible parameters for PSO but it also provides a new way to analyze particle trajectories that incorporates engineering practices. In order to validate the new strategy, we compared it with published results from three previous reports, which are consistent or approximately consistent with our new strategy, using a suite of well-known benchmark optimization functions. The experimental results show that the proposed strategy is effective and easy to implement. Moreover, the new strategy was applied to equally spaced linear array synthesis examples and compared with other optimization methods. Experimental results show that it performed well in pattern synthesis.